Concept explainers
For Exercises 1-14,
a. Write the domain.
b. Write the range.
c. Find the x-intercept(s).
d. Find the y-intercept.
e. Determine the asymptotes if applicable.
f. Determine the intervals over which the function is increasing.
g. Determine the intervals over which the function is decreasing.
h. Match the function with its graph.
1.
(a)
To find the domainof the function
Answer to Problem 1PRE
The domain of function
Explanation of Solution
Given: The function
Formula Used:
The domain of a function is the set of input or argument values for which the function is real and defined.
Calculation:
The function has no undefined points nor domain constraints. So, the domain will be all real numbers.
Therefore, the domain is
Conclusion:
The domain of function
(b)
To find the range of the function
Answer to Problem 1PRE
The range of function
Explanation of Solution
Given: The function
Formula Used:
The range of a function is the set of values of the dependent variable for which a function is defined.
Calculation:
Here, the function
Conclusion:
The range of function
(c)
To find x-intercept of the function
Answer to Problem 1PRE
There is no x-intercept
Explanation of Solution
Given: Function -
Formula Used:
x-intercept is a point on the graph where
Calculation:
The y-intercept of a function is obtained at the point when
But,
So, there is no such value of x which gives
Conclusion:
Hence, there are no x-axis interception points.
(d)
To find the y-intercept of the function
Answer to Problem 1PRE
The y-intercept of function
Explanation of Solution
Given: Function -
Formula Used:
y-intercept is a point on the graph where
Calculation:
Function is given as
For y-intercept,
And
Thus, y-axis interception point is
Conclusion:
The y-intercept of function
(e)
To find Asymptotes (if applicable) of the function
Answer to Problem 1PRE
There are no asymptotes of the function
Explanation of Solution
Given: Function -
Formula Used:
If
Calculation:
Given function is
There are no asymptotes as polynomial functions of degree 1 or higher can’t have asymptotes.
Conclusion:
Hence, there is no asymptote for the function
(f)
To find intervals over which the function
Answer to Problem 1PRE
Function is not an increasing function.
Explanation of Solution
Given: Function -
Formula Used:
If
Calculation:
Derivative of
Thus, the function is not increasing.
Conclusion:
Hence, function is not an increasing function
(g)
To find intervals over which the function
Answer to Problem 1PRE
Function is not a decreasing function.
Explanation of Solution
Given: Function -
Formula Used:
If
Calculation:
Derivative of
Thus, the function is not decreasing.
Conclusion:
Hence, the function is not a decreasing function
(h)
To graph the function
Explanation of Solution
Given: Function -
Graph:
Given function is
When
When
Thus, the graph is matched with the function
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Chapter 4 Solutions
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